An hour after Alcione Santos’s alarm goes off at 5.50am she walks to the corner where the bus stops … or will do if it’s not full already. “I might wait 10 minutes, I might wait 30, because there’s no timetable so you never know,” she explains. If the first bus is crammed beyond capacity, or breaks down, the long wait means she’ll be late for work.

Like most of metro São Paulo’s 20 million residents, Alcione can only afford to live on the periphery of South America’s biggest city. The vast sprawl and decades of underinvestment in public transport mean many face daily commutes of three, four, even five hours to get to low-paid jobs in the centre. Almost 70% of journeys are made by bus, and in places like Itaquaquecetuba in the extreme east where Alcione lives it is the only link to work and money.

She has agreed to let us join her commute. A battered bus arrives at 7am belching diesel fumes and we stand for the bumpy 30-minute ride to the train station with builders and cleaners, nurses and street sellers. As we pass through metro São Paulo’s endless edgelands of favelas and concrete box houses, car workshops and faded graffiti, passengers try to sleep despite the potholed roads and stop-start hills.

“There are 300,000 people in Itaquaquecetuba but not enough jobs,” says Alcione, who works five days a week as a poorly paid intern at the state prosecutor’s office downtown and studies law in the evenings. She puts in two 12-hour shifts as a hairdresser on weekends.

Alcione left school at 14 to sell fizzy drinks and after a few years found herself living in an illegal “occupation” on the edge of the city, with wooden shacks and open sewers. After her daughter was born she tried a few times to take adult education classes to finish school but the long hours commuting and working on her feet proved too gruelling.

“I used to leave at 5am to get to work at 8am selling plastic rubbish bags, first on the streets, and later direct to shops. At that time the buses and trains into the city are packed. It is the worst time of the day. Some rich people in São Paulo think we are on the bus because we don’t work hard enough but they should try it.”

Gabriela Vuolo of urban mobility network Cidade dos Sonhos says the poor state of the bus system is invisible unless you go to the periphery. “They are crowded and dirty, there are not enough buses and not enough routes. They break down a lot and don’t reach all the little areas where people need them. They are expensive too. It’s a complete mess.”

Anger over proposed fare hikes sparked violent protests in 2013, which grew to encompass a range of grievances and spread to 80 cities in Brazil’s biggest demonstrations for more than two decades. One man was killed in São Paulo when a frustrated car driver rammed the crowd and many people, including journalists, were hit by rubber bullets. There were more clashes over bus fares last year, with riot police firing tear gas on protesters.

By 7.35am Alcione is on her feet again on the 15-mile train ride from Manoel Feio to the downtown station of Brás. Some people are messaging on their smartphones but most stand and stare with the bleary look of the sleep-deprived. Those lucky enough to get a seat shut their eyes or bury their faces in a rucksack on their lap. Few people talk. It’s usually quiet, explains Alcione, apart from when food sellers hawk fried snacks through the carriages, amplifying their sales patter through phone speakers.

No room to get in … Alcione Santos tries to board the metro. Photograph: Nick Van Mead

We’re packed in pretty tight and there are no women-only carriages here. Alcione says that when she when she was younger she was frequently sexually harassed. If she wore a dress to work men would often press themselves against her; when she moved away they would push harder. “It happened all the time,” she says. “I get a lot of lewd comments because I’m black and it’s not a safe environment for women. One friend fell asleep on the way to work and woke to find a man pressed against her, kissing her neck.” These assaults are rarely reported, though. “People suffer but as soon as they are off the train they forget about it. The police would just laugh.”

Maybe it’s no surprise that some super-rich navigate the city by helicopter, rarely setting foot on its car-choked streets. As well as the world’s largest bus fleet, São Paulo also reputedly has the most helicopters. There are more than 450 helipads on the roofs of skyscrapers, making it possible to fly from a luxury apartment block to an office in the Itaim Bibi financial district, charter a chopper to swanky Jardins for lunch, then back to work and home again, all without ever touching the pavement.

Sky-high skimming over the city has been opened up to more people this summer with the introduction of Voom, a kind of “Uber for helicopters”, where aircraft are booked through a smartphone app. When I flew into Guarulhos airport in the east during morning rush hour last week I took a Voom to the centre. A journey that can take 90 minutes by car – and costs Alcione more than two hours by bus, train and metro – took me and my fellow passengers 10 minutes.

A car is a more achievable aspiration for most in São Paulo. Alcione says she would drive if she could afford it, although that is a long way off. “Public transport is so bad that the first thing people do when they have a little money is buy a car,” says Gabriela Vuolo. “Or a motorbike, one of those really polluting 50cc ones, they are an epidemic out in the periphery. There’s something cultural I think about car ownership. People really believe their car is going to make them happy – that it’ll make them more powerful, more comfortable, more successful, more beautiful. They think, ‘If I’m going to spend three hours in a traffic jam I’d rather be on my own, listening to my own music.’”

There is hope though. A survey in September by Cidade dos Sonhos and Rede Nossa São Paulo found that 82% of drivers said they would switch to public transport if the service was better.

That was the aim of the previous mayor, the academic Fernando Haddad. He painted a network of cycle and bus lanes on the city’s central streets, and lowered speed limits. Traffic casualties fell 20% between 2014 and 2015.

A wave of anger against the corruption-embroiled Workers Party saw him defeated and replaced by businessman and former Apprentice host João Doria, who campaigned on the slogan Acelera São Paulo (“speed up São Paulo”). One of his first acts was to raise speed limits on the expressways where Haddad had lowered them. He says he is not against bike lanes or dedicated bus routes but quickly ordered the removal of a couple of key examples, and introduced a law which makes it harder to gain approval for new bike lanes.

At 8.25am Alcione’s train pulls into Brás station and we start the slow shuffle through packed walkways to the metro platform. Sometimes you get carried along with the crush and don’t need to walk, she says.

We reach the platform 10 minutes later but the first two trains are already packed so tight that only one or two people manage to shove their way on. We squeeze our way on to the third train for an eye-to-armpit ride to Sé.

The metro system is fast and efficient but woefully overcrowded in peak hours. System coverage is also poor, with 12 feet of track per 1,000 inhabitants – a 15th as much as London, for example. The focus tends to be on wealthier areas, with promised extensions and new lines bogged down by delays. A new route to Guarulhos airport was supposed to open in 2014. It now looks like summer 2018.

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It takes us 15 minutes to navigate the crowded station and fight our way across the congested city streets, but we finally make it to Alcione’s office just after 9am – 2 hours and 10 minutes after she left home.

Alcione will work all morning, study all afternoon and attend classes in the evening. At 10pm she’ll reverse the trip – getting home by 11.30pm if she’s lucky – ready to repeat it all six hours later.

“The trouble is that everything is in central São Paulo,” she says. “It’s a big problem for the kids. As they grow up they have to work to help support their family but if they spend four hours a day standing on buses they are too tired to keep up with school work and they drop out. It is a vicious cycle.”